Fluid starting point
You could do this by adjusting the offset value of the fluid simulation.

Here's a short summary of this: 

Go to the offset settings of the Blender fluid domain (Assuming you are using Blender v2.81 or before), and adjust the value to a higher number to make the simulation happen earlier, and lower to happen later.

This will cause your fluid to show up later or earlier depending on the offset value. For a detailed answer to a similar question, look here.